Non-contact and economical position determinations are made possible by a combination of a commercially available magnet or magnetic strip with a magnetic-field sensor (typically a Hall element). If the magnetic-field source is rotatably seated relative to the sensor, then such an arrangement enables a non-contact angle determination. On the other hand, if the magnetic-field source is movable linearly along a movement axis, then a one-dimensional position determination is possible. There is a fundamental difference in this context between unipolar and bipolar arrangements, depending on whether a single magnetic pole or several magnetic poles are used for measurement.
FIG. 1A shows a bipolar arrangement of a magnetic-field source N, S and a magnetic-field sensor SM1. The magnetic-field source N, S is, for example, a bar magnet and is movable relative to the magnetic-field sensor SM1 along a movement axis X. The magnetic-field sensor SM1 is ordinarily a Hall element. A characteristic measurement curve for the described arrangement is shown in FIG. 1A. The graphic shows the magnetic-field strength B (measured in mT) plotted against positions (measured in mm) along the movement axis X. The resulting magnetic-field function BX has several characteristic points. The minimum of the magnetic field BMIN corresponds to the minimum of the magnetic-field function BX and the maximum of the magnetic field BMAX corresponds to the maximum of the magnetic-field function BX. These points correspond in a certain sense to the individual poles of the magnetic-field source N, S. The magnetic-field function BX runs nearly linearly and through the magnetic origin B0 between the minimum and the maximum BMIN, BMAX of the magnetic field. The magnetic-field origin B0 is characterized by the fact that the magnetic-field function BX is ideally zero there. The magnetic-field origin B0 further characterizes the case in which the magnetic-field source N, S is centered above the magnetic-field sensor SM1 along the movement axis X. In practice, the measured value of the magnetic-field function BX at this point is not equal to zero, but is instead influenced by secondary effects such as temperature and production tolerances of the magnetic-field sensor SM1, as well as the distance between the magnetic-field sensor SM1 and the magnetic-field source N, S (the so-called air gap). Due to these effects, the signal from the magnetic-field sensor SM1 is generally not equal to zero.
The central parameter for applications of the bipolar and unipolar sensor arrangements for angle and position determination is the resolution (for a given air gap). The resolution is in turn dependent on a gain G of the sensor arrangement, which is determined by the output voltage VOUT of the magnetic-field sensor SM1 and by the magnetic-field strength B:
  G  =            VOUT      B        .  
For an optimal gain G and thus an optimal resolution, it is particularly important to remain in the linear range of the magnetic-field function BX over a movement range XMIN, XMAX of the magnetic-field source N, S. For this it is necessary to know a minimum endpoint XMIN of the movement of the magnetic-field source N, S and a maximum endpoint XMAX. By suitable selection of the movement range XMIN, XMAX, the full scale range FSR of the sensor arrangement between an upper and a lower full scale range limit FSRMIN, FSRMAX of the magnetic-field sensor SM1 can be filled. The lower and upper full scale range limits FSRMIN, FSRMAX are generally dependent on the magnetic-field sensor SM1 in use, as well as on the components for signal processing that are used. The terms full scale range or full scale range limits of the sensor arrangement, or simply full scale range and full scale range limits, are used below in this sense.
FIG. 1B shows a characteristic magnetic field curve BCH, which is derived from the output voltage VOUT of the magnetic-field sensor SM1 as a function of the magnetic-field strength B. Since the magnetic-field sensor SM1 is generally itself a ratiometric sensor (such as a Hall element), the magnetic-field strength B is proportional to the position along the movement axis X. The objective is now to position the full scale range FSR inside the movement range XMIN, XMAX of the magnetic-field source N, S in such a manner that the magnetic-field characteristic curve BCH is as linear as possible or lies on an ideal linear characteristic curve BLIN completely inside the measuring range FSR.
Conventional sensor arrangements of the type presented above perform a compensation of the sensitivity and of air gap variations at power-on and initially travel through the entire movement range XMIN, XMAX. The sensitivity is adjusted or set by the user based on characteristic measurement values. In the ideal case, a mechanical zero position inside the movement range XMIN, XMAX is identical with the magnetic origin B0, so that the ideal linear characteristic curve BLIN results and is optimal in the full scale range FSR. Due to mechanical tolerances, however, the movement range XMIN, XMAX is mostly not optimally centered and the full scale range FSR is not suitably utilized.
Based on these effects, the sensitivity of the sensor is generally reduced in such a manner that as large an area of the characteristic curve BCH as possible lies inside the full scale range. Thereby, however, the gain and thus the possible resolution of the sensor arrangement are reduced. For a movement range XMIN, XMAX of ±250 μm and a mechanical displacement of ±100 μm, for example, a reduction of the resolution of the system by almost a factor of 2 results. The reduction of sensitivity alone also does not guarantee that the corresponding magnetic-field characteristic curve BCH is sufficiently linear inside the full scale range FSR.